CUET UG Chemistry Booster Test – 3 Measurement and Applications of Conductivity

According to NCERT: Rearranging: Given: Substituting: Since: Therefore, the cell constant of the conductivity cell is: This method is commonly used in laboratories because the conductivity of standard KCl solutions is accurately known.

The cell constant is theoretically given by: where l is the distance between electrodes and A is their area of cross-section. In practice, conductivity cells use platinized platinum electrodes. These electrodes are coated with platinum black, producing rough and irregular surfaces. Because of this irregularity, accurate measurement of the effective electrode area becomes difficult. Similarly, exact determination of the distance between electrode surfaces is not easy. NCERT therefore recommends determining the cell constant experimentally using standard KCl solutions whose conductivity values are known accurately at different temperatures and concentrations. This method provides more reliable and reproducible results than direct geometric measurement.

In a balanced Wheatstone bridge: Rearranging: This equation is used to determine the resistance of the conductivity cell containing the electrolyte solution. The Wheatstone bridge provides accurate resistance measurements because the balance condition eliminates the effect of current through the detector branch. Once R₂ is known, conductivity can be calculated using the cell constant. Therefore, the correct expression is:

According to NCERT: where: and After the Wheatstone bridge measurement, the resistance of the conductivity cell is known. Substituting the measured resistance and known cell constant into the above formula gives the conductivity. Because conductivity increases as resistance decreases, the relationship is inverse. Therefore, conductivity is calculated by dividing the known cell constant by the measured resistance.

From the definition of resistivity: Rearranging: Thus Statement 1 is correct. Conductivity is the reciprocal of resistivity: Hence Statement 2 is correct. Conductance is: Combining the conductivity and conductance relationships: Therefore Statement 4 is correct. Statement 3 is incorrect because it reverses the correct relationship between conductance and conductivity. Thus Statements 1, 2 and 4 are correct.

For conductivity: because: For molar conductivity: since: Similarly: For resistivity: These conversions are frequently used in conductivity calculations and numerical problems in electrochemistry. Therefore, the correct matching is: 1-c, 2-a, 3-b, 4-d.

According to NCERT, molar conductivity is defined as the conductance of the volume of solution containing one mole of an electrolyte when placed between electrodes separated by unit distance and having a sufficiently large area of cross-section. Unlike conductivity, which refers to the conductance of a unit volume of solution, molar conductivity refers specifically to the conductance associated with one mole of electrolyte. As concentration decreases, a larger volume of solution is required to contain one mole of electrolyte. Therefore, molar conductivity represents the conductance of that particular volume of solution which contains exactly one mole of the dissolved electrolyte. Hence, Option B correctly describes the physical meaning of molar conductivity.

When conductivity is expressed in SI units (S m⁻¹) and concentration is expressed in mol m⁻³, molar conductivity is given by: This formula directly relates conductivity to the concentration of electrolyte in the solution. The factor of 1000 appears only when concentration is expressed in mol L⁻¹ and conductivity in S cm⁻¹. Since SI units are used here, no conversion factor is needed. Molar conductivity therefore represents the conductivity contribution per mole of electrolyte dissolved in the solution. Hence: is the correct expression.

Conductivity is a measure of the conductance of a unit volume of solution. As an electrolyte solution is diluted, ions become distributed throughout a larger volume. Although dilution increases ionic mobility and may increase the degree of dissociation of weak electrolytes, the number of ions present per unit volume decreases substantially. This reduction in charge carriers dominates the conductivity behavior. Consequently, conductivity decreases with dilution for both strong and weak electrolytes. In contrast, molar conductivity increases because it refers to the conductance associated with one mole of electrolyte rather than one unit volume of solution. Therefore, conductivity decreases because the decrease in ion concentration per unit volume outweighs the increase in mobility or dissociation.

Weak electrolytes such as acetic acid are only partially dissociated in solution. At higher concentrations, a significant fraction of the electrolyte remains in the undissociated form. Upon dilution, the equilibrium shifts toward greater ionization. Consequently, the degree of dissociation (α) increases substantially. As more ions are produced, the number of charge carriers available for conduction increases. Because molar conductivity depends on both ionic mobility and the number of ions present, the sharp rise in α causes a steep increase in molar conductivity. This effect is much more pronounced than in strong electrolytes, which are already almost completely dissociated. Therefore, the steep increase in molar conductivity is primarily due to the increase in the degree of dissociation.

For strong electrolytes, NCERT gives: The constant A depends on the type of electrolyte, particularly the charges carried by the ions. Electrolytes are classified as: • 1–1 type → NaCl • 2–1 type → CaCl₂ • 2–2 type → MgSO₄ As ionic charges increase, interionic attractions become stronger. Consequently, the magnitude of A increases. Thus: Corresponding to: 2 < 3 < 1 Hence the correct order is: NaCl → CaCl₂ → MgSO₄.

For strong electrolytes such as KCl: This equation has the form of a straight line. Therefore: • Statement 1 is correct because Λm versus √c is linear. • Statement 2 is correct because extrapolation to zero concentration gives Λ°m. • Statement 3 is incorrect because the slope is negative, not positive. • Statement 4 is correct because the magnitude of the slope corresponds to the constant A. The graph is one of the most important graphical representations in electrochemistry and is used to determine limiting molar conductivity experimentally.

For a weak acid: where: c = concentration in mol L⁻¹ α = degree of dissociation Since α is dimensionless, the unit of Ka is determined entirely by the concentration term. Therefore: Conductivity measurements are used to determine α through: After α is calculated, Ka is obtained from the above equilibrium expression. Thus, the usual unit of Ka is mol L⁻¹.

Although weak electrolytes become highly dissociated near infinite dilution, the number of ions present per unit volume becomes extremely small because the solution is highly dilute. Conductivity depends on the number of charge carriers per unit volume. Therefore, despite increased dissociation, the conductivity value becomes very low. At such low concentrations, experimental measurement of conductivity becomes difficult and less accurate. This is one reason why limiting molar conductivity for weak electrolytes cannot be obtained directly by extrapolation of conductivity data. Thus, the conductivity becomes so small that accurate measurements are challenging.

The degree of dissociation is defined as the fraction of electrolyte molecules that dissociate into ions. For weak electrolytes: As concentration approaches zero, interionic interactions disappear and the electrolyte becomes completely dissociated. Therefore: and hence: This means that at infinite dilution, the electrolyte behaves as if it is fully ionized. Thus, the degree of dissociation approaches unity.

In electrochemistry: represents the limiting molar conductivity of an individual cation. represents the limiting molar conductivity of the entire electrolyte at infinite dilution. denotes the degree of dissociation of a weak electrolyte. represents the dissociation constant of a weak acid. These symbols are extensively used in Kohlrausch's law, Ostwald's dilution law and conductivity calculations. Understanding their meanings is essential for solving numerical and conceptual problems in electrochemistry. Therefore the correct matching is: 1-b, 2-d, 3-c, 4-a.

Kohlrausch's Law of Independent Migration of Ions states that at infinite dilution, each ion contributes independently to the limiting molar conductivity of an electrolyte. Mathematically: This law makes it possible to calculate the limiting molar conductivity of weak electrolytes such as acetic acid using conductivity data of strong electrolytes. For example: Thus, Kohlrausch's law is widely used in conductivity measurements and determination of dissociation constants.

Consider: Adding the first two equations and subtracting the third: The ions Na⁺ and Cl⁻ cancel mathematically, leaving: which equals: Therefore, Na⁺ and Cl⁻ are eliminated.

The determination of the dissociation constant of a weak electrolyte follows a logical sequence. First, the molar conductivity at a known concentration is measured experimentally. Next, the limiting molar conductivity is obtained using Kohlrausch's law because weak electrolytes do not permit direct extrapolation. The degree of dissociation is then calculated: Finally, Ostwald's dilution law is used: Therefore, the correct sequence is: Measure Λm → Determine Λ°m → Calculate α → Calculate Ka. Corresponding to: 2 → 4 → 3 → 1.

For acetic acid, conductivity measurements are first performed at concentration c to obtain Λm. Since acetic acid is a weak electrolyte, its Λ°m cannot be obtained accurately by extrapolating its own Λm versus √c graph because the plot is highly curved near low concentrations. Instead, Λ°m is determined indirectly using Kohlrausch's law and the limiting molar conductivities of strong electrolytes. The degree of dissociation is then calculated: As concentration decreases, dissociation increases, causing α to increase. Therefore, Statements 1, 3 and 4 are correct, while Statement 2 is incorrect.